At a Palm Beach, Fla. estate, Romney told big-money donors he'll "probably eliminate for high-income people" the mortgage interest deduction on second homes, as well as deductions for state income and property taxes. "By virtue of doing that, we'll get the same tax revenue, but we'll have lower rates," he said, in remarks overheard by NBC News and the Wall Street Journal.

A big mystery of Romney's tax pledge -- to "cut tax rates across the board by 20 percent" and reduce the corporate tax rate from 35 percent to 25 percent -- is what tax loopholes he'll close to pay for the cost.

Romney's tax cuts are projected to cost the federal government $5 trillion over 10 years, on top of the $4 trillion 10-year cost of making the Bush tax cuts permanent. Existing deductions and exemptions in the tax code, all together, reduce receipts by about $1 trillion per year, according to estimates.

Chuck Marr, director of federal tax policy at the Center on Budget and Policy Priorities, said all the deductions Romney proposed to scrap "would pay for less than 20 percent" of the $5 trillion cost of his tax plan. "The deductions he unveiled would raise less than $1 trillion," he said.

Romney's mortgage interest proposal would yield "probably less than 1 percent of the total cost" of his tax cuts, Marr said, while axing the state and local deduction for everyone, which would be very difficult to enact politically, would yield about $800 billion to $900 billion over 10 years. "So that'd be a major step but still pay for a small share of his tax cuts," Marr said.

It's unclear whether Romney would eliminate these expenditures entirely or simply cap them, to limit the extent to which they benefit high-income earners.

The deductibility of home mortgage interest and the tax exemption for employer-provided health care eat up a big chunk of the $1 trillion in revenue the government loses annually because of tax expenditures. Both are very popular politically, and they've become fundamental to the country's housing and health care policy. Other perks, like the low capital gains rate and oil and gas subsidies, are backed by powerful constituencies that both parties, but particularly Republicans, are at pains to scale back.

The Romney campaign backed away from the remarks Monday morning, suggesting they're aware the bad math could become a political liability. "He was just discussing ideas that came up on the campaign trail," Romney surrogate Jim Talent told reporters on a conference call Monday. "He wasn't announcing a policy yesterday. We don't have any plans now to announce new policies."

That has given Romney's political opponents ammunition to fire away at his tax plan.

"I'm not sure how much stock we should put into overheard remarks at a fundraiser, but even if these were the two deductions he would eliminate, they wouldn't come close to offsetting the tax cut he wants to give to the rich," said Seth Hanlon, director of fiscal reform at the Center for American Progress Action Fund. "It's a small fraction of filling the fiscal hole he'd have dug."